Kernel

What is the benefit of using symmetric kernel in Fourier transform?

What is the benefit of using symmetric kernel in Fourier transform?
  1. What is symmetric kernel?
  2. Is Fourier kernels are separable and symmetric?
  3. What is the kernel of Fourier transform?
  4. Why is FFT symmetric?

What is symmetric kernel?

1.1 Symmetric kernel

A complex valued kernel k(x, t), a ≤ x, t ≤ b is called a symmetric or Hermitian kernel of an integral equation if k(x, t) = k(t, x), where the bar denotes the complex conjugate. In this situation, the integral equation is also called a ”symmetric integral equation”.

Is Fourier kernels are separable and symmetric?

It is easily shown that the inverse Fourier kernel is also Separable and symmetric.

What is the kernel of Fourier transform?

Any kernel K (x,y) of an integral transform which may be written in the form K (x,y) = k (xy) and which is identical with the kernel of the inverse transform.

Why is FFT symmetric?

Because both the positive and negative frequency sinusoids are 90 degrees out of phase and have the same magnitude, they will both respond to real signals in the same way.

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